Answers
The composite figure has an area of 26 square units.
How to determine the area of a composite figure
In this question we find a composite figure formed by the sum of the areas of two right triangles and rectangles, whose area formulas are shown below:
Right triangle
A = 0.5 · w · l
Rectangle
A = w · l
Where:
w - Width, in unitsl - Length, in unitsNow we proceed to determine the area of the composite figure:
A = 0.5 · 3 · 1 + 3 · 1 + 0.5 · 3 · 1 + √10 · √40
A = 1.5 + 3 + 1.5 + 20
A = 26
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Related Questions
Connie deposits $30 into an account. The value of the account, in dollars, can be modeled as V(t) = 30 (1. 05)^t , where t is the time, in years, since opening the account.
To the nearest cent, What is the average rate of change in the value of the account for the first 3 years?
A. $0. 63/year
B. $1. 58/year
C. $3. 15/year
D. $4. 73/year
Answers
If Connie deposits $30 into an account. The average rate of change in the value of the account for the first 3 years is: B. $1. 58/year.
How to find the average rate of change?Given data:
Equation V(t) = 30 (1. 05)^t
Where,
t = time, in years, since opening the account = 3 years
Average rate of change = [30 (1. 05)^t] - 30/3
Average rate of change = [30 (1. 05)^5] - 30/3
Average rate of change = ($34.73 - $30)/3
Average rate of change = (#4.73)/3
Average rate of change = $1.58
Therefore the correct option is B.
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10. The vertical motion formula h = -16t² + vt, gives the height of a projectile, h, at any
time, t, for a starting velocity, v. Find the number of seconds it takes for a rocket
launched with a starting velocity of 96 ft/s to reach an altitude of 45 ft. Algebraic
solutions only. Round answers to the nearest tenth.
Answers
The number of seconds it takes for a rocket launched with a starting velocity of 96 ft/s to reach an altitude of 45 ft is t = 3/2 or t = 4.
What is Velocity?
The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.
Let's begin with the equation for projectile motion, which is h = vt - 16t2.
h is the object's height in this formula.
The initial velocity is v, and the time is t.
We are aware that the starting speed is 80 feet per second.
so that we can substitute an 80 in our formula for v.
We also know that the item rises 96 feet above the ground.
ground, allowing us to substitute an integer of 96 for h in our formula.
The result is 96 = 88t - 16t2.
We set this equation's value to 0 in order to solve it by
16t2 - 88t + 96 = 02. 16t2 - 88t + 96 = 02.
We may now divide both sides by 8 to obtain the result 2t2 - 11t + 12 = 0.
To achieve (2t - 3(t - 4) = 0, we may now factor the left side.
This implies that either 2t - 3 = 0 or t - 4 = 0.
Hence, t = 3/2 or t = 4.
Since the item will be, there are two possible answers.
Both when going up and down, it was 96 feet above the ground.
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Need answer for these questions
Answers
Using Pythagoras Theorem, the lengths are 1)3√8 cm 2)2[tex]\sqrt{65}[/tex] cm 3) 8√2 cm and 4) 12 cm.
What is Pythagoras Theorem?Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.
1) Here the diagonal of the square is the hypotenuse.
Base length = 6 cm and Altitude length = 6 cm
(Diagonal length)² = 6² + 6²
= 72
Diagonal length = √72 = 3√8 cm
2) Longest side is the hypotenuse.
Length of longest side = [tex]\sqrt{14^2+8^2}[/tex] = [tex]\sqrt{260}[/tex] = 2[tex]\sqrt{65}[/tex] cm
3) When height divides the triangle into two, there are two right angled triangles.
Height is the altitude of the right angled triangle.
Hypotenuse is 12 cm and base is half of 8 cm.
Height² = 12² - 4²
Height² = 128
Height = [tex]\sqrt{128}[/tex] = 8√2 cm
4) Here, the base of the isosceles triangle is twice the base of the right triangle.
Base² = 10² - 8² = 36
Base of the right triangle = √36 = 6 cm
Base of the isosceles triangle = 2 × 6 = 12 cm
Hence using Pythagoras theorem, all the lengths are found.3
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Solve the system of equations using substitution or elimination. Include step-by-step explanation, please!
Answers
We can solve the system of equations by using the elimination method, the solution is:
x = 5.25
y = -1.75
How to solve the system of equations?Here we want to solve the system of equations:
x + y= 3.5
x - y = 7
To solve it, we can use the elimination method. To do it, we can add/subtract the equations in such a way that one of the variables gets eliminated.
I will directly add the two equations.
(x + y) + (x - y) = 3.5 + 7
x + x + y - y = 10.5
2x = 10.5
Now we can solve this for x.
x = 10.5/2
x = 5.25
Replacing that in one of the equations, we will get:
x - y = 7
5.25 - y = 7
5.25 - 7 = y
-1.75 =y
The solution for the system of equations is:
x = 5.25
y = -1.75
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Which of the following expressions is equivalent to (4m²-8m+12) - (5m³-m-
-9)
m² + 7m-21
-m²-9m+3
m²-9m-3
-m²-7m+21
16
Answers
Expressions is equivalent to -m²-7m+21.
What expressions work similarly?Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value for the variable is entered, two algebraic expressions that are equivalent will have the same result.
When reduced to their most basic form, two or more ratios are said to be similar if their values are the same. Equivalent ratios include 1:2, 2:4, and 4:8. In their simplest form, all three ratios have the same value of 1:2.
Since both expressions' values are constant for all values of x, the equivalent expressions 3(x + 2) and 3x + 6 are also identical expressions. 3x + 6 = 3 × 4 + 6 = 18.
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What is the distance from (- 2 4 to 0 )? Round your answer to the nearest hundredth?
Answers
20 units is the required distance between the two given points (-2, 4) and (0, 0).
What is the distance?The measurement of distance is the separation between two objects or points, and it can be quantitative or occasionally qualitative.
In physics, the term "distance" can refer to a physical length or, more commonly, to an estimate based on several other parameters.
The distance between two locations on a plane is the length of the line segment connecting them.
The formula d=((x2 - x1)2 + (y2 - y1)2) is frequently used to determine the separation between two points.
So, we know that the distance formula is as follows:
d=((x2 - x1)2 + (y2 - y1)2)
The given points are: (-2, 4) and (0, 0)
Insert values in the formula to calculate the distance as follows:
d=((x2 - x1)2 + (y2 - y1)2)
d=((0 - (-2))2 + (0 - 4)2)
d= (2)2 + (-4)2
d = 4 + 16
d = 20
Therefore, 20 units is the required distance between the two given points (-2, 4) and (0, 0).
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The difference of c and 6 is greater than or equal to -26
Answers
A phrase, "the difference of c and 6 is greater than or equal to -26" as an expression, is c - 6 ≥ -26.
What is an expression?A term is a single mathematical phrase. It might consist of only one variable-a letter-one number-positive or negative-or several variables multiplied but never added or subtracted. A number is placed in front of some nouns that have variables. The number used before a sentence is called a coefficient.
Given:
A phrase: The difference of c and 6 is greater than or equal to -26.
The difference of c and 6 can be expressed as,
c - 6.
And c - 6 is greater than or equal to -26 can be expressed as,
c - 6 ≥ -26.
The expression is c - 6 ≥ -26.
Therefore, the phrase can be expressed as c - 6 ≥ -26.
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What is the description method of sinigang? (description set po in mathematics)
PLEASE HELP THANK YOU!!
Answers
Answer:
cooking method
Step-by-step explanation:
I am not sure if you mean the food or not
'S' is the incenter, so what type of segments are drawn?
A. Perpendicular Bisectors
B. Medians
C. Angle Bisectors
D. Altitudes
Answers
'S' is the incenter, so Angle Bisectors type of segments are drawn.
What is Angle Bisectors?The line or line segment that divides an angle into two equal pieces is known as the (interior) bisector of the angle, also known as the internal angle bisector (Kimberling 1998, pp. 11–12). An angle bisector divides the opposite side of a triangle into two portions that are proportional to the other two sides, according to the angle bisector theorem.One bisector exists for every angle. An angle bisector has points that are equally spaced apart from its sides. An angle's interior or internal bisector is a line, half-line, or line segment that divides an angle of less than 180° into two equal angles.To learn more about Angle Bisectors refer to;
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What is a hyperbola graph?
Answers
Hyperbola is a smooth graph lying in a plane, having two branches, which are mirror images of each other and connected to one end and continues infinitely.
Hyperbola is a conic section, two right angled cones are intersected at a certain angle.
The main components of hyperbola is. Foci (It has two foci), Centre of hyperbola ( The midpoint of two foci of the hyperbola), Major axis, Minor axis, Vertices, Latus rectum of hyperbola, eccentricity
The equation of hyperbola is [tex]\frac{x^{2}}{a{2} }-\frac{y^{2} }{b^{2} } = 1[/tex]
All hyperbola has two graphs, which is two curves with separate vertex and focus.
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Make a mapping diagram for each relation.
{(2, 8), (-1, 5), (0, 8), (-1, 3), (-2, 3)}
Answers
Answer: A mapping diagram is a way to visualize a relation by plotting its ordered pairs on a coordinate plane.
For the relation {(2, 8), (-1, 5), (0, 8), (-1, 3), (-2, 3)}, the mapping diagram would look like this:
(x,y)
(-2,3) (-1,3)
(0,8)
(-1,5) (2,8)
In the above diagram, each point represents an ordered pair from the relation. You can see that the relation maps x-coordinates -2, -1, 0, 1 and 2 to y-coordinates 3,3,8,5 and 8 respectively.
Step-by-step explanation:
Mabel has a 15 year adjustable rate mortgage with a fixed rate for the first 4 years. In the 5th year, the Interest rate rises to 5. 8%. The
remaining balance at the end of the 4th years is $231,975. 40. What is the monthly payment in the 5th year? (4 points)
Answers
The monthly payment in the 5th year is $2,005.18
To calculate the monthly payment in the 5th year of the adjustable rate mortgage, you would need to know the remaining balance of the loan at the beginning of the 5th year, the interest rate for the 5th year, and the loan term (number of remaining payments) for the 5th year. With the given information, you can calculate the monthly payment using the following formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where:
M = monthly payment
P = remaining balance at the beginning of the 5th year
i = interest rate for the 5th year (expressed as a decimal)
n = loan term for the 5th year (number of remaining payments)
Given that the remaining balance at the end of the 4th year is $231,975.40, and the interest rate for the 5th year is 5.8%
i = 5.8% / 12 = 0.004833
n = (1512) - (412) = 108
M = 231975.40 [ 0.004833(1+ 0.004833)^108] / [(1 + 0.004833)^108 -1]
M = $2,005.18
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Sam and two friends put letters in envelopes on Monday.
The three of them take two hours to put 600 letters in envelopes.
Working at the same rate, how much longer would it take four people to put 1000 letters in envelopes than it would take five people?
(4 marks)
Answers
Answer:30 minutes
Step-by-step explanation:
600/3=200
200/2=100
5x100=500
1000/500=2
4x100=400
1000/400=2.5
2.5-2=0.5hours
jeff will pick a card at random from ten cards numbered 1 through 10. the number on this card will indicate his starting point on the number line shown below. he will then spin the fair spinner shown below (which has three congruent sectors) and follow the instruction indicated by his spin. from this new point he will spin the spinner again and follow the resulting instruction. what is the probability that he ends up at a multiple of 3 on the number line? express your answer as a common fraction.
Answers
Answer:
my
Step-by-step explanation:
namajeff
Apply the distributive property to factor out the greatest common factor. 27 − 18r =?
Answers
The greatest common factor of 27 − 18r = 9(3-2r).
What is the greatest common factor?
In mathematics, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero.
Here, we have
Given: 27 − 18r
We have to determine the greatest common factor by applying the distributive property.
Distributive property = multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. i.e a × (b + c) = (a × b) + (a × c)
27 − 18r = 9(3-2r)
Hence, the greatest common factor of 27 − 18r = 9(3-2r).
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NEED HELP
This graph shows a proportional relationship.
What is the constant of proportionality?
Enter your answer as a ratio in simplified form by filling in the boxes.
Answers
The constant of proportionality from the proportional relationship is 3/2
What is Proportional RelationshipA proportional relationship is a mathematical relationship between two variables in which their ratio is always equal. In other words, if x and y are in a proportional relationship, then y/x is always equal to a constant value, called the constant of proportionality. This can be expressed mathematically as y = kx, where k is the constant of proportionality and x and y are the variables in the relationship.
To determine the constant of proportionality, we need to use the proportional relationship given.
y = kx
k = constant of proportionality
3/8 = k(1/4)
Solve for k
k = [(3/8) / (1/4)]
k = 3/2
k = 1.5
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you drive 60 miles north, then 34 miles west, then 20 miles south. how far are you from where you started?
Answers
The minimum distance from the starting point is 52.5 miles
First you travels 60 miles north as shown in the image, then 34 miles west and 20 miles south. We can draw a straight line from the endpoint to the stating point.
We could construct a triangle as shown in the figure. From that we can see that AC is the minimum distance from the start. AC is the hypotenuse of the triangle we have drawn..
To calculate the hypotenuse, we can use the Pythagoras theorem.
Hypotenuse² = base²+alt²
AC² = BC²+ AB²
= 34²+40² = 2756
AC = √2756 = 52.497 = 52.5 miles
So the minimum distance is 52.5 miles.
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Fins the degree of polynomial 3x^4-0x^3+0x^5
Answers
The degree of polynomial 3x^4-0x^3+0x^5 is 4
How to determine the degree of a polynomial?Degree of a polynomial is the highest power that its terms pertain (for multi-variables, the power of term is addition of power of variables in that term).
Therefore, inx^3+3x+5, the degree of the polynomial is 3 as the highest power in its terms is 3. (power and exponent are same thing);
Given in the question;
Polynomial= 3x^4-0x^3+0x^5
The highest degree from observation is of 3x that is equal to 4
Hence, the correct degree will be 4
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At a carnival, you spin a spinner that has four equal-sized sections, each a different color: green, yellow, red, and blue. if you land on green, you win 2 points. if you land on yellow, red, or blue, you lose 1 point. write the expected value equation. e (v) = startfraction 1 over a endfraction (2) startfraction 1 over b endfraction (c) startfraction 1 over d endfraction (e) startfraction 1 over f endfraction (g)
Answers
Answer:
a = 4
b = 4
c = -1
d = 4
e = -1
f = 4
g = -1
Step-by-step explanation:
that should be right
What is the shape of the base of a right circular cylinder?
Answers
The shape of the base of a right circular cylinder is circle.
What is right circular cylinder?
The definition of a right circular cylinder is a cylinder with a closed circular surface, two parallel bases on either end, and elements that are perpendicular to the base. Right cylinder is another name for it. The distance between each point on the closed circular surface of a right circular cylinder and the cylinder's axis, which is a straight line, is constant. The two circular bases of the right circular cylinder are parallel to one another and have the same radius. It is a certain geometric shape that is widely utilised in everyday life.
The diagram of a right circular cylinder is attached below and it can be observed that the base is circular in shape.
Hence, the shape of the base of a right circular cylinder is circle.
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6. The strike zone is the space through which a pitch must pass in order to be called a strike, even if the batter doesn't swing. In 1969, the strike zone was
shortened. What effect did this have?
A. Batters struck out less, and their batting averages improved
O B. Batters struck out more, and their batting averages got worse.
OC. Batting statistics stayed about the same, but pitching statistics improved
OD. Batting statistics stayed about the same, but pitching statistics got worse
Answers
Batters struck out more, and their batting averages got worse. The correct option is B
What is a strike zone?Strike zone is the area over home plate between the batter's knees and mid-chest where a pitched ball is considered a "strike" if it crosses the plate within this area and the batter does not swing.
The location and size of the strike zone is specified in the official rules of Major League Baseball and other baseball organizations and it is used to determine the outcome of each pitch in a game.
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What is the length of hypotenuse if base 6cm and height 8 cm in a right-angled triangle?
Answers
The length of the hypotenuse is 10 cm.
Pythagoras' Theorem is the way in which you can find the missing length of a right-angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), the Opposite (which doesn't touch the hypotenuse), and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a²+b²=c²
However, it can also be written in the form of c²=a²+b²
In order to find the hypotenuse, you will have the length of two sides, for example, these could be 3 and 4.
As 'C' is always the hypotenuse, you have to work out the two other lengths, and you do this by squaring the numbers.
3²=9 and 4²=16.
As you're looking for C, you've got to add these together
9+16=25
As a²+b²=c², this means that the answer for C is the square root of 25.
√25= 5
Let the length of the hypotenuse be represented by l, the base be represented by b and the height be represented by h.
We are given that b = 6 cm and h = 8 cm.
Using Pythagoras' theorem,
l² = b² + h²
Substitute the values,
⇒ l² = 6² + 8²
⇒ l² = 36 + 64
⇒ l² = 100
∴ l = 10
Thus, the length of the hypotenuse is 10 cm.
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in a certain lottery, three numbered balls are randomly drawn from a large basket without replacement. to win, a player's ticket must have each of the numbers drawn in no particular order. the balls are numbered from one to one hundred. if jack buys twenty-one tickets, what is the probability that he will win?
Answers
The probability that Jack will win is 0.00015. The result is obtained by dividing the number of tickets that Jack has by the total number of events.
How to calculate the probability?Probability of an event is calculated by dividing the number of favorable outcomes by the total number of events in the sample space.
In a certain lottery are 100 balls numbered from 1 - 100 in a large basket. Three numbered balls are randomly drawn without replacement. To win the lottery, a player's ticket must have each of the numbers drawn in no particular order.
If jack buys 21 tickets, find the probability that he will win!
In any the order, the different triples of tickets that a player can have can be found by a combination.
The total number of events would be
[tex]= \: _{100}C_{3}[/tex]
[tex]= \frac{100!}{3! \:97!} }[/tex]
[tex]= \frac{98 \times 99 \times 100}{2 \times 3}[/tex]
= 161700 different triples
Jack has 21 tickets. So, the probability that Jack will win is
P = 21/161700
P = 0.00013
Hence, Jack will win with the probability of 0.00013.
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What is the quotient when x3 − 5x2 3x − 8 is divided by X − 3?
Answers
The quotient of a division problem is found by dividing the dividend by the divisor.
What is a Quotient?When two numbers are divided, the outcome is referred to as the quotient in mathematics. The dividend is the quantity that is being divided. The divisor is the quantity by which we divide. We will have a remnant if the divisor is not a dividend factor.
One other perspective on the quotient exists. Keep in mind that division is simply repeated subtraction. Therefore, the quotient indicates how many times the dividend can be reduced by the divisor.
This demonstrates the interconnectedness of the four fundamental arithmetic operations. It will be demonstrated later in the session how multiplication can be used to verify the quotient in a division problem.
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a word phrase that represents m + 8.
Answers
Answer:
see explanation
Step-by-step explanation:
m + 8
can be expressed as
the sum of m and 8
Please help solve for missing side!
Answers
Answer:
Step-by-step explanation:
Use the Pythagoras Theorem to find x
Pythagoras theorem = [tex]a^2 + b^2 = c^2[/tex]
In this case a is 10 c is 20 b is x
Remember that the longest side of a triangle is always named as c
[tex]10^2 + b^2 = 20^2\\100 + b^2 = 400\\b^2 = 400-100\\b^2 = \sqrt{300}\\ b = 17.32\\[/tex]
suppose a person claims​ that, 2.1​​% of all people in the nation always eat​ out. is this a descriptive or inferential​ statement?
O Descriptive O Inferential
Answers
The statement describes the percentage of people in the nation who eat out without making any inferences or assumptions.
The statement made by the person is a descriptive statement. This means that the statement simply describes the percentage of people in the nation who always eat out. It does not make any assumptions or inferences based on the data or evidence given. A descriptive statement is one that simply states facts or information without making any assumptions or interpretations about it. It is important to note that a descriptive statement does not imply any cause and effect relationship between the facts or data given. For example, in this statement, there is no inference being made that the people who eat out are healthier or more likely to be successful than people who don't eat out. It is simply stating the percentage of people in the nation who always eat out.
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What is the factor of 8x2 12x?
Answers
The factors of the polynomial 8x^2 + 12x are (4x) and (2x + 3x).
A factor of a polynomial is a polynomial that when multiplied by another polynomial results in the original polynomial. The factor of 8x^2 + 12x is a polynomial that when multiplied by another polynomial results in 8x^2 + 12x.
To find the factors of 8x^2 + 12x, we can use different methods such as the factoring by grouping or by finding the common factor.
One possible factorization of 8x^2 + 12x is (4x)(2x) + (3x)(4x).
Taking out the common factor 4x :
8x^2 + 12x = (2x + 3x)(4x)
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What is the perimeter of the following kite?
Answers
The perimeter of the following kite is 32.
What do a kite's area and perimeter measure?Perimeter is the total of the sides, whereas area is half the product of the diagonals. Remember that a kite is a quadrilateral with distinct adjacent congruent sides and that a rhombus is a quadrilateral with four congruent sides.
How big is a quadrilateral kite's perimeter?The sides of each pair can be added to determine the kite's perimeter. Kite is another name for a quadrilateral with two sides that are equally long on either side. Therefore, a kite's perimeter is equal to 2(a+b), or twice the length of its two sides.
parameter = 2(a+b)
P = 2[(3+3) + (6+4)]
P = 2(6 + 10)
P = 32.
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What are steps in factoring?
Answers
The general steps to factor a composite number are dividing the composite number by the smallest prime number, if the division is exact, you have found one of the factors of the composite number.
After that then divide the quotient by the smallest prime number that is greater than the divisor used in step 1. Repeat this step with the quotient until the quotient is a prime number. The prime factors of the composite number are the divisors used in the previous steps and the quotient obtained in step 4.
Factoring is the process of finding the prime factors of a composite number.
For example, if you want to factor the composite number 60, you would begin by dividing 60 by 2. Since 60 is divisible by 2, we know that 2 is a factor of 60. The quotient is 30.
We will then divide 30 by 3 and got 10 as quotient.
Then we divide 10 by 2 and got 5 as quotient. 5 is a prime number, so we know that the prime factors of 60 are 2 x 3 x 5
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